Suppose you are interested in estimating the ceteris paribus relationship between final exam scores (y) and class attendance (x1). You can also collect data on two control variables, x2 and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on x1 only and B represent the estimate from the full regression with all controls. (a) If class attendance is highly correlated with both controls, and both controls have a large effect on y, would you expect the two estimates to be similar or very different? Why? (b) If class attendance is uncorrelated with the two controls, but the two controls are highly

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4. Suppose you are interested in estimating the ceteris paribus relationship between final exam
scores (y) and class attendance (x1). You can also collect data on two control variables, x2
and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on
x1 only and B1 represent the estimate from the full regression with all controls.
(a) If class attendance is highly correlated with both controls, and both controls have a large
effect on y, would you expect the two estimates to be similar or very different? Why?
(b) If class attendance is uncorrelated with the two controls, but the two controls are highly
correlated with each other, will the two estimates tend to be similar or different? Why?
(c) If class attendance is highly correlated with the two controls, and the two controls have
very small effects on y, do we expect the two estimates to be similar or different on
average? Why?
Transcribed Image Text:4. Suppose you are interested in estimating the ceteris paribus relationship between final exam scores (y) and class attendance (x1). You can also collect data on two control variables, x2 and x3, which could be GPA and SAT scores. Let B1 be the bivariate regression estimate on x1 only and B1 represent the estimate from the full regression with all controls. (a) If class attendance is highly correlated with both controls, and both controls have a large effect on y, would you expect the two estimates to be similar or very different? Why? (b) If class attendance is uncorrelated with the two controls, but the two controls are highly correlated with each other, will the two estimates tend to be similar or different? Why? (c) If class attendance is highly correlated with the two controls, and the two controls have very small effects on y, do we expect the two estimates to be similar or different on average? Why?
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